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arXiv · 2208.08325

Algebraic Cycles and values of Green's functions

Ramesh Sreekantan
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Abstract

We construct indecomposable cycles in the motivic cohomology group $H^3_{{\mathcal M}}(A,{\mathbb Q}(2))$ where $A$ is an Abelian surface over a number field or the function field of a base. When $A$ is the self product of the universal elliptic curve over a modular curve, these cycles can be used to prove algebraicity results for values of higher Green's functions, similar to a conjecture of Gross, Kohnen and Zagier. We formulate a conjecture which relates our work with the recent work of Bruinier-Ehlen-Yang on the conjecture of Gross-Kohnen-Zagier.

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Ramesh Sreekantan. 2022-08-17. Algebraic Cycles and values of Green's functions. https://arxiv.org/abs/2208.08325

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